Polycondensation Kinetics: 2. Time-Dependent29Si NMR Spectra of Poly-Dimethyldimethoxysilane

Abstract

The polycondensation of dimethyldimethoxysilane has been studied by 29Si NMR to high degrees of conversion at pH 2.8. The relative concentrations of nonbonded Si atoms (D0) and bound by one (D1) and two (D2) Si–O–Si bonds have been determined from the integrated intensities of the multiplets assigned to them. The measurement results have been considered in terms of the kinetic scheme proposed in the first paper. It has been found that the D0(t), D1(t), and D2(t) curves coincide with those measured for the ratio of the constants of competing processes of aggregation and addition of monomers k ≈ 0.15. The time-dependent molecular mass distributions have been determined with allowance for chain termination during the formation of cyclic and entangled oligomers.

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Funding

This work was carried out under Presidium Program P22 of the Russian Academy of Sciences and in accordance with the topic of State assignment no. 0089-2019-0008.

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Correspondence to V. A. Benderskii.

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Translated by S. Zatonsky

Appendices

APPENDIX

CYCLIZATION AND ENTANGLEMENT WITH RANDOM CHAIN GROWTH IN THE LATTICE

Since the structure of monodisperse colloidal particles of SiO2 [22] is close to the structure of a SiO2 crystal [23], we consider polycondensation as the sequential formation of a chemical bond between the end of the growing chain and one of the “free” sites in its nearest neighborhood that has a reactive group capable of forming this bond. According to the Flory hypothesis [24], the probability of bond formation does not depend on the length of the previously formed chain and the number of free sites, so that the calculation of the rate constants reduces to a combinatorial calculation. Termination occurs when a cycle is formed in which two end sites are combined. In a simple cubic lattice, the smallest cycle is tetramer C4, in which the sites of one of the faces are combined (top panel of Fig. 5). If edge 12 of this face is selected as the initial direction of growth, the formation of the cycle includes the successive formation of edges 23, 34, and 41. Edge 23 can be equally probable in four directions perpendicular to 12, so that its formation probability is 4/5. The fifth direction, shown by the dotted line, leads the end group out of the immediate environment of group 1. The cycle is formed if the edges 34 and 41 are uniquely directed, i.e. with a probability of 1/5. Thus, the formation probability of C4 is (1/5) 4/5. The next cycle, hexamer C6, is formed if the chain is directed in four directions other than edge 41; i.e., the probability of avoiding bond 41 is 4/5. The following uniquely directed edges form a face perpendicular to the face C4 so that the C6 formation probability is (1/5)3 (4/5)2. A similar calculation determines the formation probability of the cyclic octamer C8, (1/5)4 (4/5)3. The probability of cyclization with further growth of n leads to (6). At n ≥ 8, as shown by the structure on the right in the second panel, in addition to cyclization, there is entanglement, which reduces the number of “free” sites. The cycles and the entangled structure at n = 12 are shown on the bottom panel.

Fig. 5.
figure5

Schematic representation of cyclic and entangled n-mers with different chain lengths. Top panel: the formation of cyclic tetramer C4. The open circle indicates initial site 1, and double line 12 shows the initial direction of chain growth. The possible directions of the edges are shown by thin arrows. The dashed arrow indicates the direction of growth that avoids cyclization. Middle panel: the formation of octamer C8. For the right structure, entanglement reduces the number of directions avoiding cyclization from 4 to 2. Bottom panel: the formation of C12. Entanglement occurs in planar structures as well. On the right, the complete entanglement of the starting site is shown.

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Kim, I.P., Chernyak, A.V. & Benderskii, V.A. Polycondensation Kinetics: 2. Time-Dependent29Si NMR Spectra of Poly-Dimethyldimethoxysilane. High Energy Chem 54, 155–163 (2020). https://doi.org/10.1134/S001814392003008X

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Keywords:

  • polycondensation
  • poly-DMDMOS
  • time-dependent 29Si NMR spectra
  • linear and cyclic oligomers